期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 275, 期 -, 页码 310-322出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2014.07.004
关键词
Electrostatic correlation; Variational field theory; Green's function; Poisson-Boltzmann theory; Fast algorithm; Sparse matrix; Selected inversion
资金
- Natural Science Foundation of China [11101276, 91130012]
- Alexander von Humboldt Foundation
- Agence Nationale de la Recherchevia the project FSCF
Electrostatic correlations and fluctuations in ionic systems can be described within an extended Poisson-Boltzmann theory using a Gaussian variational form. The resulting equations are challenging to solve because they require the solution of a high-dimensional nonlinear partial differential equation for the pair correlation function. This has limited existing studies to simple approximations or to one-dimensional geometries. In this paper we show that the numerical solution of the equations is greatly simplified by the use of selective inversion of a finite difference operator which occurs in the theory. This selective inversion preserves the sparse structure of the problem and leads to substantial savings in computer effort. In one and two dimensions further simplifications are made by using a mixture of selective inversion and Fourier techniques. With the help of numerical examples, we validate the accuracy of the numerical method and show that electrostatic correlations and fluctuations could lead to a large deviation from the classical Poisson-Boltzmann equation with the increase of the coupling parameter. (C) 2014 Elsevier Inc. All rights reserved.
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